Evolutionary tuning of sigma-point Kalman filters

The Kalman filter is widely used but the tedious and time-consuming tunings of the filter parameters must be unavoidably carried out before use, and frustratingly, after every reconfiguration on the sensors. In this paper, we formulated the measurement residual in a performance index, and utilised an evolutionary method to automatically and efficiently calibrate the parameters of the sigma-point Kalman filter. Without analytically resolving the nonlinear and multivariate process and measurement models in the filter, the proposed method implicitly solves for the filter parameters in a gradient-free manner through a series of strategies including the selection, crossover and shuffling mutation. Furthermore, to demonstrate the superior performance of the method, we applied this method to a highly nonlinear and coupled state estimation problem on an unmanned helicopter which experiences a GNSS outage. The empirical results showed that the proposed method not only automated and significantly accelerated the exhausting tweaking of the filter parameters, but also yielded a high quality tuning result that strikingly outperformed an earlier, painstakingly handcrafted calibration.